Roller shade with a pretensioned spring and method for pretensioning the spring

ABSTRACT

A roller shade is disclosed having a counterbalancing assembly with an optimally pretensioned spring that lowers the torque load on the motor of the roller shade throughout the rolling up or rolling down cycles. The roller shade comprises a roller tube, a gudgeon pin having a first stop, a gudgeon body having a through bore and rotatably connected about the gudgeon pin and operably connected to the roller tube, a limit nut operably connected to the gudgeon body and adapted to axially travel along the gudgeon pin within the through bore, a spring, a first spring carrier connected to the first end of the spring and operably connected to the gudgeon pin, and a second spring carrier connected to the second end of the spring and operably connected to the roller tube. The spring is pretensioned and the limit nut abuts the first stop thereby locking the pretension. Rotation of the roller tube to roll down the shade further tensions the spring, and rotation of the roller tube to roll up the shade releases the tension in the spring.

BACKGROUND OF THE INVENTION

Technical Field

Aspects of the embodiments generally relate to roller shades, and moreparticularly to systems, methods, and modes for counterbalancing aroller shade with pretensioned spring and method for pretensioning thespring to lower the torque load on the motor of the roller shadethroughout the rolling up or rolling down cycles of the roller shade.

Background Art

Motorized roller shades provide a convenient one-touch control solutionfor screening windows, doors, or the like, to achieve privacy andthermal effects. A motorized roller shade typically includes arectangular shade material attached at one end to a cylindrical rotatingtube, called a roller tube, and at an opposite end to a hem bar. Theshade material is wrapped around the roller tube. An electric motor,either mounted inside the roller tube or externally coupled to theroller tube, rotates the roller tube to unravel the shade material tocover a window. To uncover the window, however, a lot of torque andmotor power are required to initially lift the entire weight of theshade material and the hem bar. This is in particular detrimental tobattery operated motors as rolling up the shade quickly drains thebattery.

Various methods exist for counterbalancing roller shades using springsmounted inside the roller tubes in an effort to reduce torquerequirements on shade motors. As the roller shade is unraveled, tensionbuilds up in the spring. The tension is released when the roller shadeis rolled up, thereby assisting the motor in lifting the shade material.One approach uses a conventional torsion spring comprising a pluralityof coils. As a torsion spring is wound up, it builds up torque. When thetorsion spring is let go, the amount of torque exerted by the torsionspring progressively reduces in a linear fashion as the torsion springwinds down. FIG. 1A shows a diagram 100 representing the performance ofa conventional torsion spring in assisting rolling up an exemplary sizedroller shade. Line 105 represents the torque profile necessary to rollup an exemplary sized roller shade from a rolled down position, when theshade material is fully unraveled, up to a rolled up position, when theshade material is fully wrapped about the roller tube. Initially, moretorque is required to lift the entire weight of the fully unraveledshade material and the hem bar as represented by maximum torque(T_(max)) value 102. As the roller tube turns, the shade material wrapsaround the roller tube, resulting in less shade material hanging fromthe roller tube. Accordingly, as the roller tube keeps turning, lesstorque is required to lift the weight of the remaining shade materialuntil a minimum torque (T_(min)) value 103 is reached. Line 106represents the torque exerted by the torsion spring during the rollershade travel. As shown, the torsion spring torque 106 decreases at aslope in a linear fashion to a zero value as the torsion spring windsdown.

Currently, a torsion spring is chosen with a torque 106 that approachesthe T_(max) value 102 required to lift the shade material and the hembar. The resulting torque, shown by line 108 in the figure, required tobe exerted by the motor to roll up the roller shade is equal to thedifference between the torque of the roller shade 105 and the springtorque 106. FIG. 1B shows a diagram 101 representing the resulting power110 required of the motor to roll up the shade. As the roller shadebegins to roll up from a fully unrolled position, the torsion springreleases its built up torsion energy. Then its energy progressivelydiminishes as the roller shade continues to roll up. At the end of therolling up cycle, the torsion spring unravels back to zero torsionassistance. Thus, a conventional torsion spring assists the motorsignificantly more when the roller shade begins to roll up than duringthe remainder of the rolling up cycle. In the example of FIGS. 1A and1B, initially about 0.1 N m of torque and less than 1 W of power arerequired to lift up the roller shade. That number climbs up to above 0.8N m of torque and above 6 W of power at the end of the roll up cycle.Thus, while the conventional torsion spring decreases the amount oftorque required to roll up the roller shade in the beginning, the amountof torque and power required to finish rolling up the roller shaderemains quiet high.

Counterbalancing systems exist that pretension the spring in the rollershade to further assist in rolling up the roller shade. One such systemallows pretensioning the spring during the installation of the rollershade. However, field pretensioning is often done incorrectly, leavingthe customer unsatisfied with the performance of the product. Therefore,it is desired to have a factory settable pretension of a spring. Othersystems exist that allow factory settable pretensioning by providingmeans that temporary hold the pretension until the roller shade isinstalled. Thereafter, the pretension is held by the weight of the shadematerial. However, this preset pretension often dissipates during thecontinual operation of the shade, when the shade is knocked down or hitaccidentally, or when the shade needs to be removed and reinstalled.Other systems required complex field adjustment and complicatedmotorized pretensioning.

Therefore, a need has arisen for systems, methods, and modes forcounterbalancing a roller shade with a pretensioned spring and methodfor pretensioning the spring to lower the torque load on the motor ofthe roller shade throughout the rolling up or rolling down cycles of theroller shade. Additionally, a need has arisen for systems, methods, andmodes for counterbalancing a roller shade with pretensioned spring thatcan be pretensioned at the factory to a preset amount and which locksand continuously maintains the pretension.

SUMMARY OF THE INVENTION

It is an object of the embodiments to substantially solve at least theproblems and/or disadvantages discussed above, and to provide at leastone or more of the advantages described below.

It is therefore a general aspect of the embodiments to provide systems,methods, and modes for counterbalancing a roller shade with pretensionedspring and method for pretensioning the spring to lower the torque loadon the motor of the roller shade throughout the rolling up or rollingdown cycles of the roller shade.

It is also an aspect of the embodiments to provide systems, methods, andmodes for counterbalancing a roller shade with pretensioned spring thatcan be pretensioned at the factory to a preset amount and which locksand continuously maintains the pretension.

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used to limit the scope of the claimed subject matter.

Further features and advantages of the aspects of the embodiments, aswell as the structure and operation of the various embodiments, aredescribed in detail below with reference to the accompanying drawings.It is noted that the aspects of the embodiments are not limited to thespecific embodiments described herein. Such embodiments are presentedherein for illustrative purposes only. Additional embodiments will beapparent to persons skilled in the relevant art(s) based on theteachings contained herein.

DISCLOSURE OF INVENTION

According to one aspect of the embodiments, a roller shade is provided,comprising: a roller tube; a gudgeon pin comprising a first stop and asecond stop; a gudgeon body rotatably connected about the gudgeon pinand operably connected to the roller tube, wherein the gudgeon bodycomprises a through bore; a limit nut operably connected to the gudgeonbody and adapted to axially travel along the gudgeon pin, within thethrough bore, and between the first stop and the second stop; a springlongitudinally extending from a first end to a second end; a firstspring carrier connected to the first end of the spring and operablyconnected to the gudgeon pin; and a second spring carrier connected tothe second end of the spring and operably connected to the roller tube.

According to another aspect, the rotation of the roller tube to rolldown the roller shade causes rotation of the second end of the spring ina first direction with respect to the first end of the spring, therebytensioning the spring. Further, rotation of the roller tube to roll upthe roller shade causes rotation of the second end of the spring in asecond direction, opposite to the first direction, with respect to thefirst end of the spring, thereby releasing the tension in the spring.The roller shade can be rolled up or rolled down by pulling or tuggingon a hem bar, by pulling on a chain, or via a motor.

In another embodiment, the spring comprises a pretensioned spring andthe limit nut abuts the first stop or the second stop thereby lockingpretension in the pretensioned spring. In some aspects of theembodiments, during pretensioning of the pretensioned spring, the rollershade comprises: (i) the second spring carrier positioned within theroller tube such that the second spring carrier is operably connected tothe roller tube; (ii) the gudgeon body positioned outside the rollertube; (iii) the gudgeon body rotating with respect to the roller tube,thereby causing the limit nut to rotate and axially travel in a firstdirection, until the limit nut comes in contact with the first stop orthe second stop; (iv) after the limit nut comes in contact with thefirst stop or the second stop, the gudgeon body further rotating withrespect to the roller tube a predetermined number of pretension turns,thereby causing the first spring carrier and the first end of the springto rotate with respect to the second spring carrier and the second endof the spring; and (v) the gudgeon body inserted inside the roller tubethereby locking the pretension.

In another embodiment, the gudgeon pin comprises a proximal portion, amiddle portion, and a distal portion, wherein the first stop is disposedbetween the proximal portion and the middle portion, and wherein thesecond stop is disposed between the middle portion and the distalportion. The gudgeon pin may further comprise a gudgeon pin tip disposedon a terminal end of the gudgeon pin that attaches to a mountingbracket. In another embodiment, at least one of the first stop and thesecond stop of the gudgeon pin comprises at least one of a ring, a pin,a screw, or any combination thereof. In one embodiment, the gudgeon pintravels axially within the through bore and the first stop and thesecond stop limit the axial travel of the gudgeon pin with respect tothe gudgeon body.

In another embodiment, the gudgeon body is rotatably connected about thegudgeon pin via at least one ball bearing. The gudgeon body may comprisea flange radially extending therefrom that prevents the gudgeon bodyfrom sliding entirely into the roller tube. The gudgeon body maycomprise at least one ball bearing cavity dimensioned to receive the atleast one ball bearing therein. The gudgeon body may further comprise awheel with an external surface that contacts an inner surface of theroller tube. In one embodiment, the gudgeon body comprises a pluralityof teeth extending circumferentially about an external surface of thegudgeon body that form a friction fit between the external surface ofthe gudgeon body and an inner surface of the roller tube. In anotherembodiment, the gudgeon body further comprises a plurality of channelsextending circumferentially about an external surface of the gudgeonbody that mate with complementary projections radially extending from aninner surface of the roller tube.

In another embodiment, the roller shade comprises a spring mandrelconnected to the gudgeon pin and wherein the spring is mounted about thespring mandrel. In one embodiment, the spring comprises a torsionspring.

In another embodiment, the gudgeon pin and the limit nut are threadedand wherein the limit nut is threadably connected to the gudgeon pin.The through bore may comprise a cross-section having a shape thatcomplements and mates with a shape of the limit nut. For example, thelimit nut and the cross-section of the through bore comprise at leastone of the following shapes: a hexagon, a triangle, a square, aheptagon, an octagon, and a star.

In one embodiment, the second spring carrier comprises a wheel with anexternal surface that contacts an inner surface of the roller tube. Thewheel of the second spring carrier may be dimensioned such that it isoperably connected to the roller tube and can axially travel within theroller tube. Further, the wheel of the second spring carrier comprises aplurality of channels extending circumferentially about its externalsurface that mate with complementary projections radially extending froman inner surface of the roller tube.

According to another aspect of the embodiments, a roller shade isprovided, comprising: a roller tube; a gudgeon pin comprising a firststop; a gudgeon body rotatably connected about the gudgeon pin andoperably connected to the roller tube, wherein the gudgeon bodycomprises a through bore; a limit nut operably connected to the gudgeonbody and adapted to axially travel along the gudgeon pin within thethrough bore; a spring longitudinally extending from a first end to asecond end; a first spring carrier connected to the first end of thespring and operably connected to the gudgeon pin; a second springcarrier connected to the second end of the spring and operably connectedto the roller tube; wherein the limit nut abuts the first stop when theroller shade is in a rolled up position, and wherein rotation of theroller tube to roll down the roller shade causes the limit nut toaxially travel along the gudgeon pin, within the through bore, and awayfrom the first stop. In another embodiment, the spring comprises apretensioned spring, and wherein the limit nut abuts the first stopthereby locking pretension in the pretensioned spring.

According to another aspect of the embodiments, a roller shade isprovided, comprising: a roller tube; a gudgeon pin comprising a firststop; a gudgeon body rotatably connected about the gudgeon pin andoperably connected to the roller tube, wherein the gudgeon bodycomprises a through bore; a limit nut operably connected to the gudgeonbody and axially travels along the gudgeon pin within the through bore;a first spring carrier operably connected to the gudgeon pin; a secondspring carrier operably connected to the roller tube; a pretensionedspring comprising (a) a first end connected to the first spring carrier,and (b) a second end connected to the second spring carrier; whereinduring pretensioning of the pretensioned spring, the roller shadecomprises: the second spring carrier positioned within the roller tubesuch that the second spring carrier is operably connected to the rollertube; the gudgeon body positioned outside the roller tube; the gudgeonbody rotating with respect to the roller tube, thereby causing the limitnut to rotate and axially travel in a first direction, until the limitnut comes in contact with the first stop; after the limit nut comes incontact with the first stop, the gudgeon body further rotating withrespect to the roller tube a predetermined number of pretension turns,thereby causing the first spring carrier and the first end of thepretensioned spring to rotate with respect to the second spring carrierand the second end of the pretensioned spring; and the gudgeon bodyinserted inside the roller tube thereby locking the pretension.

According to some aspect of the embodiments, the method forpretensioning the spring comprises: (i) positioning the second springcarrier within the roller tube such that the second spring carrier isoperably connected to the roller tube; (ii) positioning the gudgeon bodyoutside the roller tube; (iii) rotating the gudgeon body with respect tothe roller tube, thereby causing the limit nut to rotate and axiallytravel in a first direction, until the limit nut comes in contact withthe first stop or the second stop; (iv) after the limit nut comes incontact with the first stop or the second stop, further rotating thegudgeon body with respect to the roller tube a predetermined number ofpretension turns, thereby causing the first spring carrier and the firstend of the spring to rotate with respect to the second spring carrierand the second end of the spring; and (v) inserting the gudgeon bodyinside the roller tube thereby locking the pretension.

According to some aspects of the embodiments, the predetermined numberof pretension turns N_(p) is determined according to the followingformula:

$N_{p} = \frac{T_{min\_ offset}}{k}$

where,

-   -   T_(min) _(_) _(offset) is substantially equal to, or offset by a        predetermined amount from, a minimum amount of torque required        to finish rolling up the roller shade, and    -   k is substantially equal to a torque slope of the roller shade.        In another embodiment, the torque slope k of the roller shade is        determined according to the following formula:

$k = \frac{T_{\max} - T_{\min}}{N_{t}}$

where

-   -   T_(max) is substantially equal to a maximum amount of torque        required to start rolling up the roller shade,    -   T_(min) is substantially equal to the minimum amount of torque        required to finish rolling up the roller shade, and    -   N_(t) is a number of turns it takes to fully roll up the roller        shade.        In another embodiment, the T_(max) and T_(min) are determined        according to the following formulas:

T _(max) =r _(rt)×(w _(sm) +w _(hb)) T _(min) =r _(sm) ×w _(hb)

where,

-   -   r_(rt) is a radius of the roller tube,    -   w_(sm) is a weight of a shade material,    -   w_(hb) is a weight of a hem bar, and    -   r_(sm) is a radius of the shade material when it is fully        wrapped around the roller tube.

According to another aspect of the embodiments, a method is provided forpretensioning a spring of a roller shade including a roller tube, agudgeon pin having a first stop, a gudgeon body, a limit nut, a firstspring carrier, and a second spring carrier, the method comprising: (i)positioning the gudgeon body and the first spring carrier outside theroller tube, wherein the first spring carrier is operably connected tothe gudgeon pin and to a first end of the spring; (ii) positioning thesecond spring carrier within the roller tube such that the second springcarrier is operably connected to the roller tube, wherein the secondspring carrier is connected to a second end of the spring, (iii)rotating the gudgeon body with respect to the roller tube about thegudgeon pin, thereby causing the limit nut to rotate and axially travelin a first direction along the gudgeon pin and within a through bore ofthe gudgeon body, until the limit nut comes in contact with the firststop, (iv) after the limit nut comes in contact with the first stop,further rotating the gudgeon body with respect to the roller tube apredetermined number of pretension turns, thereby causing the firstspring carrier and the first end of the spring to rotate with respect tothe second spring carrier and the second end of the spring; and (v)inserting the gudgeon body inside the roller tube thereby locking thepretension.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects and features of the embodiments will becomeapparent and more readily appreciated from the following description ofthe embodiments with reference to the following figures. Differentaspects of the embodiments are illustrated in reference figures of thedrawings. It is intended that the embodiments and figures disclosedherein are to be considered to be illustrative rather than limiting. Thecomponents in the drawings are not necessarily drawn to scale, emphasisinstead being placed upon clearly illustrating the principles of theaspects of the embodiments. In the drawings, like reference numeralsdesignate corresponding parts throughout the several views.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

FIG. 1A illustrates a torque diagram of a prior-art roller shade using aconventional torsion spring;

FIG. 1B illustrates a power diagram of a motor required to lift theprior-art roller shade using the conventional torsion spring;

FIG. 2A illustrates a torque diagram of a roller shade using apretensioned torsion spring according to one embodiment of theinvention;

FIG. 2B illustrates a power diagram of a motor required to lift theroller shade using the pretensioned torsion spring according to oneembodiment of the invention;

FIG. 3A illustrates an end view of a roller shade in a fully rolled downposition according to one embodiment of the invention;

FIG. 3B illustrates an end view of the roller shade in a fully rolled upposition according to one embodiment of the invention;

FIG. 4 illustrates a front perspective view of a roller shade includinga counterbalancing assembly according to one embodiment of theinvention;

FIG. 5 illustrates a rear perspective view of the counterbalancingassembly according to one embodiment of the invention;

FIG. 6 illustrates an exploded front perspective view of thecounterbalancing assembly according to one embodiment of the invention;

FIG. 7 illustrates an exploded cross-sectional view of thecounterbalancing assembly according to one embodiment of the invention;

FIG. 8A illustrates a cross-sectional view of a rolling tube and thecounterbalancing assembly therein with a gudgeon pin and limit nut in afirst position according to one embodiment of the invention;

FIG. 8B illustrates a cross-sectional view of the rolling tube and thecounterbalancing assembly therein with the gudgeon pin and limit nut ina second position according to one embodiment of the invention;

FIG. 8C illustrates a cross-sectional view of the counterbalancingassembly partially extended out of the roller tube according to oneembodiment of the invention;

FIG. 9 illustrates a front perspective view of the counterbalancingassembly partially extended out of the roller tube according to oneembodiment of the invention; and

FIG. 10 illustrates a rear view of a gudgeon body of thecounterbalancing assembly according to one embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

The embodiments are described more fully hereinafter with reference tothe accompanying drawings, in which embodiments of the inventive conceptare shown. In the drawings, the size and relative sizes of layers andregions may be exaggerated for clarity. Like numbers refer to likeelements throughout. The embodiments may, however, be embodied in manydifferent forms and should not be construed as limited to theembodiments set forth herein. Rather, these embodiments are provided sothat this disclosure will be thorough and complete, and will fullyconvey the scope of the inventive concept to those skilled in the art.The scope of the embodiments is therefore defined by the appendedclaims.

Reference throughout the specification to “one embodiment” or “anembodiment” means that a particular feature, structure, orcharacteristic described in connection with an embodiment is included inat least one embodiment of the embodiments. Thus, the appearance of thephrases “in one embodiment” on “in an embodiment” in various placesthroughout the specification is not necessarily referring to the sameembodiment. Further, the particular features, structures, orcharacteristics may be combined in any suitable manner in one or moreembodiments.

LIST OF REFERENCE NUMBERS FOR THE ELEMENTS IN THE DRAWINGS IN NUMERICALORDER

The following is a list of the major elements in the drawings innumerical order.

-   100 Torque Diagram of a Roller Shade Using a Conventional Torsion    Spring-   101 Power Diagram of a Motor-   102 Maximum Torque-   103 Minimum Torque-   105 Torque Profile of a Roller Shade-   106 Torque of a Conventional Torsion Spring-   108 Torque of a Motor-   110 Power of a Motor-   200 Torque Diagram of a Roller Shade Using a Pretensioned Torsion    Spring-   202 Maximum Torque-   203 Minimum Torque-   206 Spring Rate Slope-   208 Torque of a Motor-   210 Power of a Motor-   300 Roller Shade-   301 Roller Tube-   303 Shade Material-   304 Hem Bar-   306 Roller Tube Diameter-   308 Roller Tube Radius-   310 Diameter of the Shade Material Wrapped on the Roller Tube-   311 Radius of the Shade Material Wrapped on the Roller Tube-   313 Shade Material Layers-   400 Counterbalancing Assembly-   401 a First End-   401 b Second End-   402 Gudgeon Body-   403 Gudgeon Pin-   404 First Spring Carrier-   406 Second Spring Carrier-   407 Spring Mandrel-   408 First Ball Bearing-   409 Second Ball Bearing-   410 a First Cylindrical Wheel-   410 b Second Cylindrical Wheel-   411 Cylindrical Tube-   412 a External Surface-   412 b External Surface-   413 Inner Surface-   414 Flange-   415 Teeth-   416 Channels-   417 Projections-   418 Motor-   421 Gudgeon Pin Tip-   422 Cylindrical Wheel-   423 External Surface-   426 Channels-   430 a Mounting Bracket-   430 b Mounting Bracket-   431 Mounting Hole-   441 Clockwise Direction-   442 Counterclockwise Direction-   450 Spring-   451 First End-   452 Second End-   601 Proximal Portion-   602 Middle Portion-   603 Distal Portion-   604 Threads-   605 First Stop-   606 Second Stop-   607 Limit Nut-   702 Threaded Screw Hole-   704 Threaded Screw-   706 Threads-   708 Threads-   711 First Ball Bearing Cavity-   712 Second Ball Bearing Cavity-   714 Through Bore-   715 Bore-   717 Bore-   801 Direction-   802 Direction-   901 Clockwise Direction-   902 Counterclockwise Direction-   904 Markings

LIST OF ACRONYMS USED IN THE SPECIFICATION IN ALPHABETICAL ORDER

The following is a list of the acronyms used in the specification inalphabetical order.

-   -   N mm Newton Millimeter    -   N m Newton Meter    -   N_(t) Number of Turns it Takes to Fully Roll Up the Roller Shade    -   k Torque Slope of the Roller Shade    -   r_(rt) Radius of the Roller Tube    -   r_(sm) Radius of the Shade Material When it is Fully Wrapped        Around the Roller Tube    -   T_(max) Maximum Torque    -   T_(min) Minimum Torque    -   W Watts    -   w_(hb) Weight of the Hem Bar    -   w_(sm) Weight of the Shade Material

MODE(S) FOR CARRYING OUT THE INVENTION

The different aspects of the embodiments described herein pertain to thecontext of counterbalancing and pretensioning roller shades, but is notlimited thereto, except as may be set forth expressly in the appendedclaims. While the various aspects of the embodiments are describedherein with regards to motorized roller shades, the embodiments are notnecessarily limited thereto. For example, the embodiments describedherein may be used to counterbalance and pretension manual roller shadesor semi-manual roller shades, which roll up or roll down by pulling ortugging on a hem bar or by pulling on a chain. Additionally, while theroller shade is described herein for covering a window, the roller shademay be used to cover doors, wall openings, or the like. The embodimentsdescribed herein may further be adapted in other types of window or doorcoverings, such as inverted rollers, Roman shades, Austrian shades,pleated shades, blinds, shutters, skylight shades, garage doors, or thelike.

For 40 years Crestron Electronics Inc. has been the world's leadingmanufacturer of advanced control and automation systems, innovatingtechnology to simplify and enhance modern lifestyles and businesses.Crestron designs, manufactures, and offers for sale integrated solutionsto control audio, video, computer, and environmental systems. Inaddition, the devices and systems offered by Crestron streamlinestechnology, improving the quality of life in commercial buildings,universities, hotels, hospitals, and homes, among other locations.Accordingly, the systems, methods, and modes of the aspects of theembodiments described herein, as embodied as 300 and 400 can bemanufactured by Crestron Electronics Inc., located in Rockleigh, N.J.

Disclosed herein are systems, methods, and modes for counterbalancing aroller shade with one or more pretensioned springs and method forpretensioning the springs to lower the torque load on the motor of theroller shade throughout the rolling up or rolling down cycles of theroller shade. Disclosed are also systems, methods, and modes forcounterbalancing a roller shade with one or more pretensioned springsthat can be pretensioned at the factory to a preset amount and whichcontinuously lock the pretension.

To efficiently counterbalance a roller shade, a preset number ofpretensioning turns needs to be determined for a given roller shade andits spring. In one embodiment, a torsion spring is utilized. However,other types of springs may be used without departing from the scope ofcurrent embodiments. Referring to FIG. 2A, line 105 represents theroller shade torque profile across the number of turns required to rollup an exemplary sized roller shade from a rolled down position, when theshade material is fully unraveled, up to a rolled up position, when theshade material is fully wrapped up around the roller tube. The y-axisrepresents the torque required in Newton Meter (N m) to roll up a rollershade, and the x-axis represents the number of 360 degree turns theroller shade rotates during the rolling up cycle (i.e., traveling rightalong the x-axis). Initially, more torque is required to start liftingall the weight of the shade material and the hem bar. As the roller tuberotates, the shade material wraps around the roller tube, resulting inless shade material hanging from the roller tube. Accordingly, as theroller tube keeps rotating, less torque is required to lift the weightof the remaining shade material plus the hem bar. T_(max) 102 representsthe maximum torque required to start lifting the entire weight of theshade material and hem bar, while T_(min) 103 represents the minimumtorque required to finish lifting the shade material and the hem barduring the rolling up cycle.

Line 206 represents the spring rate slope of the roller shade's spring.It is desired that the T_(max) 202 and T_(min) 203 values of the springbe set to be substantially equal to the T_(max) 102 and T_(min) 103values, respectively, of the roller shade profile 105. Alternatively, asshown in FIG. 2A, the T_(max) 202 and T_(min) 203 values of the springmay be slightly offset down by a predefined amount from the roller shadeT_(max) 102 and T_(min) 103 values, respectively. Reducing the T_(max)202 and T_(min) 203 values of the spring with respect to the rollershade T_(max) 102 and T_(min) 103 values will ensure that the shadematerial naturally drops down when the roller shade is rolled down anddoes not tend to roll back up. As shown in FIG. 2A, T_(min) 103 requiredto finish lifting the roller shade is not zero. There is always sometorque required to finish lifting the shade because of the weight of thehem bar across the width of the shade, some pulling created by the shadematerial, and the inertia and weight of the roller tube itself.Accordingly, T_(min) set point 203 of the spring has to be brought upfrom zero to substantially equal to, or slightly offset below T_(min)103 of the roller shade. This is accomplished by pretensioning thetorsion spring such that when the roller shade is fully rolled up, thetorsion spring still exerts a preset amount of torque 203 that issubstantially equal to or slightly offset below from T_(min) 103 of theroller shade.

With optimally pretensioned torsion spring, the spring assists rollingup the roller shade throughout the rolling up cycle of the roller shade.As a result, the resulting torque 208 required to be exerted by themotor to roll up the roller shade is minimal and substantially steadythroughout the rolling up cycle of the roller shade. Similarly, theresulting power 210 shown in FIG. 2B is significantly reduced and issubstantially steady throughout the rolling up cycle of the rollershade. As illustrated in the example of FIGS. 2A and 2B, the maximumtorque required to be exerted to lift an exemplary sized roller shade isbelow 0.15 N m, compared to above 0.8 N m of torque required to lift thesame sized shade by a motor with the aforementioned prior artcounterbalancing system. Similarly, the maximum power required to liftan exemplary sized roller shade is around 0.8 W, compared to 6 W ofpower required to lift the same sized shade by a motor with theaforementioned prior art counterbalancing system.

In addition, the optimally pretensioned torsion spring also assists themotor to steadily lower the roller shade throughout the entire rollingdown cycle (i.e., traveling left along x-axis in FIG. 2A).

The torque profile 105 of a roller shade depends on various propertiesof the roller shade. For example, the torque profile 105 of a rollershade varies depending on various factors, such as the roller tubediameter and radius, the diameter and radius of the shade material as itwraps about the roller tube, the shade material thickness, the width andlength of the shade material, the number of layers of the shade materialabout the roller tube, the weight of the shade material, and the weightof the hem bar. Depending on the window size and the fabric selection,the pretension parameters of the required torsion spring will change.The systems, methods, and modes of the embodiments described hereinprovide the ability to optimally pretension a torsion spring duringassembly of the roller shade at the factory by determining the optimalnumber of pretension turns for a given roller shade such that theT_(min) value 203 of the torsion spring corresponds to the T_(min) value103 of the roller shade. The embodiments described herein may be used topretension torsion springs to be used in stock roller shades sold in anumber of predetermined sizes and shade materials. The embodimentsdescribed herein may be used to quickly and precisely pretension torsionsprings to be used in customized roller shades, during the assembly ofthe customized roller shades at the factory, right after the customerhas placed their order.

To determine the preset number of pretension turns, initially the rollershade properties are determined. FIG. 3A illustrates an end view of aroller shade 300 in a fully rolled down position, and FIG. 3Billustrates an end view of the roller shade 300 in a fully rolled upposition. The roller shade properties include one or more of thediameter 306 and radius 308 of the roller tube 301, the diameter 310 andradius 311 of the shade material 303 when it is fully wrapped on theroller tube 301, the shade material 303 thickness, the width and lengthof the shade material 303, the number of layers 313 of the shadematerial 303 about the roller tube 301 when it is fully wrapped on theroller tube 301, the weight of the shade material 303, and the weight ofthe hem bar 304.

For customizable roller shades, for example, initially a customer willmeasure the window dimensions and select the style of the roller shadethey want. The customer may pick from a selection of mounting bracketsand hardware, hem bars, fabric designs, fabric attributes, such astransparency, translucency, and blackout materials, and the like. Acustomer may use the Crestron® Design Tool, a one-stop Web-basedplatform for all the Crestron® Shading Solutions designing, availablefrom Crestron Electronics, Inc. of Rockleigh, N.J. Then, the customerwill submit their order to the manufacturer. The manufacturer may usecomputer software to convert the customer requirements to manufacturingspecifications for production, as is known in the art. The manufacturingspecifications specify, for example, the diameter 306 of the roller tube301 to use, how long to cut the roller tube 301, how long and wide tocut the shade material 303, and what type of hardware to use inassembling the customized roller shade, including the type of hem bar304. All of the above customized properties will drive the weight of theroller shade, and thereby the roller shade torque profile 105.

Using the aforementioned roller shade properties, the T_(max) andT_(min) values of the roller shade 300 are determined. T_(max)represents the maximum torque required to start rolling up the rollershade 300 when the shade material 303 is fully unraveled. Thus, as shownin FIG. 3A, the entire weight of the shade material 303 plus the weightof the hem bar 304 need to be pulled up. T_(max) is determined by thefollowing formula:

T _(max) =r _(rt)×(w _(sm) +w _(hb))  (1)

where,

-   -   r_(rt) is the radius 308 of the roller tube 301, which is used        because all the shade material 303 is already unraveled,    -   w_(sm) is the weight of the entire shade material 303, and    -   w_(hb) is the weight of the hem bar 304.

T_(min) represents the minimum torque required to finish rolling up theroller shade 300 when the shade material 303 is fully wrapped around theroller tube 301. As shown in FIG. 3B, the only weight that is beinglifted at the end of the rolling up cycle is the weight of the hem bar304. T_(min) is determined by the following formula:

T _(min) =r _(sm) ×w _(hb)  (2)

where,

-   -   r_(sm) is the radius 311 of the shade material when it is fully        wrapped around the roller tube 301, and    -   w_(hb) is the weight of the hem bar 304.        Exemplary T_(max) 102 and T_(min) 103 values are illustrated in        FIG. 2A.

Using the T_(min) and T_(max) values, a slope is determined for thenatural torque profile of the roller shade. The slope is determined bythe following formula:

$\begin{matrix}{{k( \frac{N\mspace{14mu} {mm}}{turn} )} = \frac{T_{\max} - T_{\min}}{N_{t}}} & (3)\end{matrix}$

where,

-   -   k is the torque slope of the roller shade, and    -   N_(t) is the number of turns it takes to fully roll up the        roller shade.

Optionally, as discussed above, the T_(max) 202 and T_(min) 203 valuesof the spring may be offset from the natural torque profile 105 of theroller shade. This can be accomplished through a static or a percentageoffset, as follows:

T _(min) _(_) _(offset)(N mm)=T _(min)−offset  (4)

T _(min) _(_) _(offset)(N mm)=T _(min)×(1−offset_(percentage))  (5)

Once the slope and offset T_(min) 203 value are determined, the numberof preset pretension turns can be determined using the followingformula:

$\begin{matrix}{N_{p} = \frac{T_{min\_ offset}}{k}} & (6)\end{matrix}$

where,

-   -   N_(p) is the number of pretensioned turns, and    -   k is the torque slope of the roller shade.        If no offset is being made, then T_(min) _(_) _(offset) is        substituted with T_(min) 103 in the above formula. As shown, the        number of pretension turns is determined using the slope of the        natural torque profile of the roller shade to bring the minimum        torque of the torsion spring up from zero torque to the desired        minimum torque value, in this example T_(min) 203. As a result,        when the determined preset number of pretension turns are put in        the spring, T_(min) 203 of the spring is either substantially        equal to T_(min) 103 of the roller shade 300, or as shown in        FIG. 2A, it is slightly offset below T_(min) 103 of the roller        shade 300 by a predetermined amount.

The next section describes an embodiment of a roller shadecounterbalancing assembly that allows for pretensioning the torsionspring. Using the counterbalancing assembly, a torsion spring can bepretensioned at the factory to a preset number of turns as required fora particular roller shade 300 to effectively counterbalance the rollershade 300 according to the systems, methods, and modes described above.The counterbalancing assembly of the embodiments described hereinobviates field adjustments or more complicated motorized pretensioning.

Referring to FIG. 4, there is shown a front perspective view of a rollershade 300 including a counterbalancing assembly 400 according to oneembodiment. Roller shade 300 generally comprises a roller tube 301,shade material 303, hem bar 304, counterbalancing assembly 400, andmotor 418. Roller tube 301 is generally cylindrical in shape andlongitudinally extends from a first end 401 a to a second end 401 b.Assembly 400 fits within the roller tube 301 at its first end 401 a. Thesecond end 401 b of roller tube 301 includes the motor 418 that rotatesthe roller tube 301. A first end of the shade material 303 is connectedto the roller tube 301 and a second end of the shade material 303 isconnected to the hem bar 304. Shade material 303 wraps around rollertube 301. The roller shade 300 is mounted on a window via mountingbracket 430 a connected to the first end 401 a and mounting bracket 430b connected to the second end 401 b of the roller tube 301.

FIGS. 5-8C illustrate various views of the counterbalancing assembly 400in greater detail. Specifically, FIG. 5 shows a rear perspective view ofassembly 400; FIG. 6 shows an exploded front perspective view ofassembly 400; FIG. 7 shows an exploded cross-sectional view of assembly400; and FIGS. 8A-8C show cross-sectional views of assembly 400 inside aroller tube 301 in various positions. Referring to FIGS. 4-7,counterbalancing assembly 400 includes a gudgeon body 402, a gudgeon pin403, a first ball bearing 408 (FIG. 6), a second ball bearing 409 (FIG.6), a first spring carrier 404 (FIG. 6), a torsion spring 450, a secondspring carrier 406, and a spring mandrel 407.

The gudgeon body 402 of assembly 400 is rotatably connected about thegudgeon pin 403. It is inserted into the roller tube 301 and is operablyconnected to the roller tube 301 such that rotation of the roller tube301 also rotates the gudgeon body 402. The gudgeon body 402 includes apair of first and second cylindrical wheels 410 a and 410 binterconnected via a cylindrical tube 411. First and second wheels 410 aand 410 b comprise external surfaces 412 a and 412 b, respectively,which contact the inner surface 413 of the roller tube 301. First wheel410 a comprises a flange 414 radially extending therefrom. Flange 414prevents the gudgeon body 402 from sliding entirely into the roller tube301 (see FIG. 8A). First and second wheels 410 a and 410 b furthercomprise a plurality of teeth 415 and a plurality of channels 416extending circumferentially about the external surfaces 412 a and 412 bof first and second wheels 410 a and 410 b. Teeth 415 are used to form afriction fit between the external surfaces 412 a and 412 b of the firstand second wheels 410 a and 410 b, respectively, and the inner surface413 of roller tube 301. Channels 416 mate with complementary projections417 radially extending from the inner surface 413 of roller tube 301 toprevent first and second wheels 410 a and 410 b from rotating withrespect to the roller tube 301.

Referring to FIGS. 7 and 8A, the gudgeon body 402 defines a first ballbearing cavity 711, a second ball bearing cavity 712, and a through bore714 therebetween. In various embodiments, the gudgeon body 402 comprisesaluminum, stainless steel, plastic, fiberglass, or other materials knownto those skilled in the art.

Referring to FIGS. 6, 7 and 8A, the gudgeon pin 403 comprises a proximalportion 601, a middle portion 602, and a distal portion 603. Theproximal portion 601 includes gudgeon pin tip 421 disposed on theterminal end of the proximal portion 601 to attach the roller shade 300to mounting bracket 430 a. A first stop 605 is disposed on the gudgeonpin 403 between the proximal portion 601 and the middle portion 602. Asecond stop 606 is disposed on the gudgeon pin 403 between the middleportion 602 and the distal portion 603. The first stop 605 may comprisering shaped body radially extending from the gudgeon pin 403. The secondstop 606 may comprise a pin or a screw transversely extending throughthe gudgeon pin 403. Second stop 606 may be removed to allow limit nut607 to be assembled with the gudgeon pin 403. Alternatively, first stop605 may comprise a pin or a screw and second stop 606 may comprise ringshaped body. In another embodiment, stops 605 and 606 may besubstantially identical and may both comprise ring shaped bodies, pins,or screws. The middle portion 602 comprises threads 604 thereon thatrotationally receive a threaded limit nut 607. Limit nut 607 maycomprise a hexagonal cross section. Although a hexagonal limit nut 607is illustrated, other shaped nuts may be used, including but not limitedto triangle, square, heptagon, octagon, star, or the like. Limit nut 607may rotatably travel along the middle portion 602, but its travel islimited by first and second stops 605 and 606 on either side of themiddle portion 602. As shown in FIG. 7, gudgeon pin 403 furthercomprises a threaded screw hole 702 dimensioned and arranged to receivea threaded screw 704 to attach the gudgeon pin 403 to spring mandrel407. In various embodiments, the gudgeon pin 403 comprises aluminum,stainless steel, or other materials known to those skilled in the art.

The first and second ball bearings 408 and 409 generally comprise anouter race, an inner race, and a plurality of balls disposedtherebetween, as is well known in the art. In various embodiments, theball bearings 408, 409 each comprise aluminum or stainless steel. Thefirst ball bearing 408 fits within first ball bearing cavity 711 of thegudgeon body 402 and the second ball bearing 409 fits within the secondball bearing cavity 712 of the gudgeon body 402 (e.g., via friction fit,adhesive, or other means). The first ball bearing 408, through bore 714of the gudgeon body 402, and the second ball bearing 409 receive thegudgeon pin 403 therein, as shown in FIG. 8A. Particularly, the firstball bearing 408 slidably and rotationally receives the proximal portion601 of the gudgeon pin 403 and the second ball bearing 409 slidably androtationally receives the distal portion 603 of the gudgeon pin 403.First and second ball bearings 408 and 409 allow the gudgeon body 402 torotate with respect to the gudgeon pin 403 to allow the motor 418 rotatethe roller tube 301 and thereby gudgeon body 402 with respect to thegudgeon pin 403 to roll up or roll down the roller shade 300.

In addition, first and second ball bearings 408 and 409 allow thegudgeon pin 403 to travel axially with respect to the gudgeon body 402.First and second stop 605 and 606 limit the axial movement of thegudgeon pin 403 with respect to the gudgeon body 402. In other words, asshown in FIG. 8A, gudgeon pin 403 may slide out of the gudgeon body 402in direction 801 until the first stop 605 contacts the first ballbearing 408. First stop 605 prevents gudgeon pin 403 from furtherextending out of the gudgeon body 402. As shown in FIG. 8B, gudgeon pin403 may slide into the gudgeon body 402 in direction 802 until thesecond stop 606 contacts the second ball bearing 409. Second stop 606prevents gudgeon pin 403 from further extending into the gudgeon body402. In another embodiment, through bore 714 may comprise a first innerprojection or a flange at its first end that comes in contact with thefirst stop 605 and a second inner projection or a flange at its secondend that comes in contact with the second stop 606. The distance thegudgeon pin 403 may move in and out of the gudgeon body 402 isdetermined by the location of the first and second stops 605 and 606 onthe gudgeon pin 403. Second stop 606 is located at a predetermineddistance from the gudgeon pin tip 421, which is large enough to preventthe gudgeon pin tip 421 from fully extending into the gudgeon body 402.

This axial movement of the gudgeon pin 403 in and out of the gudgeonbody 402 allows for ease of installation of the roller shade 300.Typically, during the roller shade 300 mounting process, before thegudgeon pin 403 is to be coupled to a mounting bracket 430 a (FIG. 4),the second end 401 b of the roller tube 301, which includes the motor418, is mounted right up against the mounting bracket 430 b. Then, thegudgeon pin 403 is pushed into the gudgeon body 402 along itslongitudinal axis (FIG. 8B) to provide maneuvering room for aligning thegudgeon pin tip 421 with a mounting hole 431 in the mounting bracket 430a. The installation technician can then extend the gudgeon pin 403 outof the gudgeon body 402 until the gudgeon pin tip 421 is inserted andreceived by the mounting hole 431 of the mounting bracket 430 a. Inaddition, when a roller shade is installed, there needs to be sometolerance allowance within the window frame. For example, if the widthof the window frame is measured slightly wrong with respect to the widthof the roller shade 300, the axial movement of the gudgeon pin 403 maystill allow the roller shade 300 to be installed within the windowframe. Similarly, if the mounting brackets 430 a and 430 b are installedwith slightly incorrect spacing between them, the axial movement of thegudgeon pin 403 may still allow the roller shade to be installed betweenthe mounting brackets 430 a and 430 b.

Regardless of the axial position of the gudgeon pin 403 with respect tothe gudgeon body 402, as shown in FIG. 8A, the middle portion 602 of thegudgeon pin 403, the first stop 605, the second stop 606, and the limitnut 607, remain disposed within the through bore 714 of the gudgeon body402. The limit nut 607 is operably connected to the gudgeon body 402such that rotation of the gudgeon body 402 causes rotation of the limitnut 607. As shown in greater detail in FIG. 10, illustrating the rearview of the gudgeon body 402, through bore 714 comprises across-sectional shape complementary to the shape of the limit nut 607.In this example, a hexagonal limit nut 607 and a hexagonalcross-sectional shaped through bore 714 are illustrated. Although, inother embodiments, other shapes may be used as discussed above.Referring back to FIG. 8A, the limit nut 607 rotates about the middleportion 602 via threads 604 and axially travels along middle portion 602via threads 604 between first and second stops 605, 606. The hexagonallimit nut 607 mates with the hexagonal through bore 714 of the gudgeonbody 402 such that rotation of gudgeon body 402 causes rotation of thelimit nut 607. However, enough space is provided between the outersurface of the limit nut 607 and inner surface of through bore 714 suchthat limit nut 607 can axially travel within the through bore 714.

As the gudgeon body 402 rotates with respect to the gudgeon pin 403, thehexagonal inner surface of through bore 714 engages the hexagonal outersurface of limit nut 607 and causes the limit nut 607 to rotate withrespect to the gudgeon pin 403. The limit nut 607, as a result, canaxially travel along the threads 604 of the gudgeon pin 403, within thethrough bore 714, and between the first stop 605 and the second stop606. Rotating the gudgeon body 402 counterclockwise with respect to thegudgeon pin 403 causes limit nut 607 to travel in direction 801 towardsthe gudgeon pin tip 421 until it engages first stop 605, as shown inFIG. 8A. Further counterclockwise rotation of the gudgeon body 402 withrespect to the gudgeon pin 403 is hindered by the first stop 605.Rotating the gudgeon body 402 clockwise with respect to the gudgeon pin403 causes limit nut 607 to travel away from the gudgeon pin tip 421 indirection 802 until it engages second stop 606, as shown in FIG. 8B.Further clockwise rotation of the gudgeon body 402 with respect to thegudgeon pin 403 is hindered by the second stop 606.

As shown in FIGS. 4, 7, and 8A, torsion spring 450 longitudinallyextends from a first end 451 to a second end 452. Spring 450 isinstalled in the counterbalancing assembly 400 such that its first end451 is connected to the first spring carrier 404. First spring carrier404 comprises threads 706 for engaging and retaining the coils of thespring 450 at its first end 451. First spring carrier 404 is operablyconnected to the gudgeon pin 403 such that rotation of the gudgeon pin403 causes rotation of the first spring carrier 404. First springcarrier 404 comprises a bore 715 therein that receives the springmandrel 407 and the gudgeon pin 403 therein. As shown in FIG. 8A,threaded screw 704 and threaded screw hole 702 within the gudgeon pin403 lock spring mandrel 407 and gudgeon pin 403 within the bore 715 ofthe first spring carrier 404. As a result, gudgeon pin 403, first springcarrier 404, spring mandrel 407, and first end 451 of spring 450 rotatetogether with respect to gudgeon body 402 and roller tube 301. Inanother embodiment, gudgeon pin 403, first spring carrier 404, springmandrel 407, or any combinations thereof, may be constructed as a singlepiece of material. Spring 450 is mounted about the spring mandrel 407,which holds and stabilizes the spring 450 within the roller tube 301,preventing the spring 450 from sagging within the roller tube 301.

Spring 450 is connected at its second end 452 to the second springcarrier 406, which comprises threads 708 for engaging and retaining thecoils of the spring 450 at its second end 452 (FIG. 7). Second springcarrier 406 is operably connected to the roller tube 301 such thatrotation of the roller tube 301 also rotates the second spring carrier406. As shown in FIG. 4, second spring carrier 406 comprises acylindrical wheel 422 substantially similar in its outer configurationto the first and second cylindrical wheels 410 a, 410 b of the gudgeonbody 402. Wheel 422 comprises an external surface 423 that slidablycontacts the inner surface 413 of the roller tube 301. Wheel 422 alsocomprises a plurality of channels 426 extending circumferentially aboutthe external surface 423 of wheel 422. Channels 426 mate withcomplementary projections 417 radially extending from the inner surface413 of roller tube 301 to prevent wheel 422 from rotating with respectto the roller tube 301. Wheel 422 may or may not comprise teeth on itsexternal surface 423, such as teeth 415. However, wheel 422 isdimensioned and constructed such that it can axially travel within theroller tube 301 via channels 426 and projections 417. This axialtranslation allows wheel 422 to be displaced axially when the gudgeonpin 403 is inserted into or extended out of the gudgeon body 402 duringinstallation, as described above. Additionally, as the spring 450 istensioned during its pretensioning at the factory or during theoperation of the roller shade 300, it will extend or contract in length.The axial translation of second spring carrier 406 allows the spring 450to freely extend or contract in length within the roller tube 301, asrequired. In various embodiments, the first and second spring carriers404, 406 each comprise aluminum, stainless steel, plastic, fiberglass,or other materials known to those skilled in the art.

As shown in FIGS. 7 and 8A, second spring carrier 406 further comprisesa bore 717 that slidably and rotationally retains the spring mandrel407. In one embodiment, the bore 717 comprises a diameter slightlylarger than the diameter of the spring mandrel 407, and containslubricant therein such that the second spring carrier 406 may axiallytravel and rotate about the spring mandrel 407. In another embodiment,second spring carrier 406 may comprise one or more ball bearings, suchas ball bearings 408, 409, to allow smooth axial and rotational movementof the second spring carrier 406 about the spring mandrel 407.Accordingly, the roller tube 301, which is operably connected to thesecond spring carrier 406, may rotate with respect to the spring mandrel407 and the gudgeon pin 403. In addition, the second spring carrier 406may axially travel with respect to the spring mandrel 407 as the spring450 extends or contracts in length during pretensioning or operation ofthe roller shade 300.

The next section describes the method of pretensioning the roller shadein a clockwise direction using the counterbalancing assembly 400according to one embodiment. As discussed in greater detail above, apreset number of pretension turns is determined based on the rollershade properties to efficiently counterbalance the roller shade 300.During the assembly of the roller shade 300 at the factory, thetechnician is provided with the specifications of the spring 450 and theamount of turns the spring 450 has to be pretensioned. The technicianassembles the counterbalancing assembly 400 as shown in FIGS. 5 and 8Aand as discussed in greater detail above.

As shown in FIGS. 8C and 9, to pretension the torsion spring 450 in aclockwise direction 901, the second spring carrier 406 is slid insidethe roller tube 301 such that the second spring carrier 406 is operablyconnected to the roller tube 301. The gudgeon body 402 is positionedoutside of the roller tube 301. Then, gudgeon body 402 is rotated in aclockwise direction 901 while the roller tube 301 is held stationary.While the gudgeon body 402 is rotated, the channels 426 on thecylindrical wheel 422 of the second spring carrier 406 and projections417 on the roller tube 301 prevent the second spring carrier 406 fromrotating with respect to the roller tube 301. If the limit nut 607 islocated next to the first stop 605 or somewhere along the middle portion602 of the gudgeon pin 403, the rotation of the gudgeon body 402 inclockwise direction 901 causes the limit nut 607 to travel along middleportion 602 of the gudgeon pin 403 in direction 802 away from thegudgeon pin tip 421 (FIG. 8C). During this rotation, the gudgeon body402 and the limit nut 607 rotate about the gudgeon pin 403, while thegudgeon pin 403 remains stationary.

Gudgeon body 402 is rotated in clockwise direction 901 until the limitnut 607 contacts the second stop 606, as shown in FIG. 8C. In thisposition, the limit nut 607 cannot further travel with respect to thegudgeon pin 403 in direction 802. As a result, the limit nut 607 locksthe gudgeon body 402 to the gudgeon pin 403 such that gudgeon body 402can no longer rotate about the gudgeon pin 403 in a clockwise direction901. Thereby, further clockwise rotation of the gudgeon body 402 alsorotates in the clockwise direction 901 the gudgeon pin 403 as well asthe first spring carrier 404 and the spring mandrel 407. Because thespring mandrel 407 can freely rotate within the second spring carrier406 via bore 717, the first spring carrier 404 is rotated in clockwisedirection 901, while the second spring carrier 406 remains stationaryinside the roller tube 301 (FIG. 8C). This results in pretensioning thetorsion spring 450 as its first end 451, connected to the first springcarrier 404, rotates in a clockwise direction 901 with respect to itssecond end 452, connected to the second spring carrier 406.

With the gudgeon body 402 outside the roller tube 301, the limit nut 607locked with second stop 606, and starting with the torsion spring 450 ina relaxed state, pretensioning turns can be started by rotating thegudgeon body 402 with respect to the roller tube 301 until thepredetermined number of pretensioning turns is reached. In oneembodiment, the technician can use the channels 416 on the gudgeon body402 and the projections 417 inside roller tube 301 as a guide to countthe number of pretensioning turns. In another embodiment, the gudgeonbody 402 and roller tube 301 may contain markings 904 (FIG. 9) to assistthe technician to track the number of pretensioning turns made.

After the desired number of pretensioning turns is reached, the gudgeonbody 402 is inserted inside the roller tube 301, as shown in FIG. 8B,until the flange 414 of the gudgeon body 402 contacts the first end 401a of the roller tube 301. In one embodiment, the preset number ofpretension turns include full 360 degree turns. In another embodiment,the preset number of pretension turns may include less than 360 degreeincremental turns. For example, the preset number of turns couldcomprise 35.5 turns. This is achieved by allowing the gudgeon body 402to be inserted in the roller tube 301 in various radial locations.Including a plurality of channels 416 circumferentially arranged on thegudgeon body 402 and a plurality of projections 417 circumferentiallyarranged in the roller tube 301 allow the gudgeon body 402 and theroller tube 301 to be mated in various radial orientations with respectto each other. In one embodiment, the gudgeon body 402 and roller tube301 may contain a plurality of markings 904 disposed circumferentiallythereon and identifying full turns, half turns, quarter turns, or otherfractional turns.

After its assembly, the roller shade 300 is shipped out to the customerto be installed in a window. The roller shade 300 is installed in thewindow with the shade material 303 fully wrapped up around the rollertube 301 and the gudgeon pin 403 held stationary by mounting bracket 430a.

According to an aspect of the embodiments, with the gudgeon body 402inside the roller tube 301, the limit nut 607 continues to engage thesecond stop 606 locking the pretension. Particularly, while the gudgeonbody 402 is inserted in the roller tube 301 and the gudgeon pin 403 isheld stationary by mounting bracket 430 a, the first spring carrier 404,first end 451 of the spring 450, and spring mandrel 407 are also heldstationary during the operation of the roller shade 300. The pretensionof spring 450 causes the second end 452 of the spring 450 to exerttorque on the second spring carrier 406, and thereby on the roller tube301 and gudgeon body 402, in a clockwise direction 441 with respect tothe first end 451 of the spring, first spring carrier 404, and gudgeonpin 403. However, the gudgeon body 402 cannot further rotate withrespect to the gudgeon pin 403 in a clockwise direction 441 because theengagement of the limit nut 607 and the second stop 606 prevents thatrotation. Accordingly, the pretension is locked by the limit nut 607 andthe second stop 606 preventing the torsion spring 450 from unwinding.Roller tube 301 and gudgeon body 402 can, however, rotate in acounterclockwise direction 442 with respect to the gudgeon pin 403.Rotation of the roller tube 301 and gudgeon body 402 in acounterclockwise direction 442 causes limit nut 607 to travel indirection 801 (FIG. 8A) towards the gudgeon pin tip 421. In addition,the counterclockwise rotation of the roller tube 301 in direction 442rotates the second spring carrier 406 in a counterclockwise directionwith respect to the stationary first spring carrier 404, which furthertensions the torsion spring 450.

In operation, as discussed above, the roller tube 301 is pretensionedand cannot travel in a clockwise direction 441 with respect to thegudgeon pin 403. To roll down the roller shade 300, the roller tube 301is rotated by motor 418 in a counterclockwise direction 442 causing thegudgeon body 402 and second spring carrier 406 to also rotate in acounterclockwise direction 442, while the first spring carrier 404 andgudgeon pin 403 remain stationary. This causes the torsion spring 450 tofurther build torque and forces the limit nut 607 to travel in direction801 along middle portion 602 of gudgeon pin 403. The middle portion 602of the gudgeon pin 403 comprises a length large enough such that limitnut 607 does not contact first stop 605 during the rolling down cycle.In one embodiment, limit nut 607 may contact first stop 605 at the endof the rolling down cycle. The pretensioning ensures that the rollingdown cycle of the roller shade 300 starts at the desired T_(min) value203, as discussed above with reference to FIG. 2A. As the roller shade300 rolls down, torsion spring 450 continues to build torque in a linearfashion (traveling left along the x-axis in the diagram of FIG. 2A)until the T_(max) value 202 is reached. As the roller shade 300 rollsdown, the shade material 303 gradually unravels and progressively moreshade material 303 hangs down from the roller tube 301. The increasingweight of the shade material 303 and the hem bar 304 combined withtorque exerted by the spring 450 assist the motor 418 to build torque inthe torsion spring 450 throughout the rolling down cycle without themotor 418 requiring to exert much power, as shown by the exerted motortorque 208 and power 210.

When rolling up the shade 300, the torque that was built up in thetorsion spring 450 during the rolling down cycle assists the motor 418to roll up the shade 300 during the rolling up cycle. The torque exertedby spring 450 assists the motor 418 during the entire rolling up cycle(traveling right along the x-axis in the diagram of FIG. 3A). As theroller shade 300 rolls up, torsion spring 450 releases torque in asubstantially linear fashion until the T_(min) value 203 is reached. Thedecreasing weight of the shade material 303 and the hem bar 304 combinedwith the progressively released torque by the spring 450 effectivelyassist the motor 418 to roll up the roller shade 300 throughout therolling up cycle without the motor 418 requiring to exert much power, asshown by the exerted motor torque 208 and power 210. Spring 450 assiststhe motor 418 to finish rolling up the shade material 303 all the waythrough the end of the rolling up cycle because the torque of thetorsion spring 450 does not return to zero, but returns to the T_(min)value 203 as a result of the pretension.

At the end of each rolling up cycle, the pretension put into the spring450 continues to be locked as the limit nut 607 continues to engage thesecond stop 606 when the roller shade 300 is in a rolled up position.The pretension continues to be locked even if the roller shade 300 isknocked down or hit accidentally, or when the shade needs to be removedand reinstalled. The roller shade 300 may be easily serviced by a fieldtechnician or repaired as the roller shade may be easily disassembledand the factory specified pretension turns may be put back into thespring 450.

According to further aspects of the embodiments, pretensioning of theroller shade 300 can be accomplished in a counterclockwise direction ina substantially similar manner as discussed above, but with rotation ofthe gudgeon body 402 in a counterclockwise direction with respect to theroller tube 301 until limit nut 607 contacts and locks with the firststop 605 as shown in FIG. 8A. Then, a predetermined number ofcounterclockwise pretension turns can be put into the spring 450.Pretension of the roller shade 300 is locked in a counterclockwisedirection and the roller shade can rotate in a clockwise direction toroll down the shade material 303, and in a counterclockwise direction toroll up the shade material 303 in substantially the same way asdiscussed above.

Aspects of the embodiments of the roller shade 300 allow the rollershade 300 to be assembled and installed as a standard roll or a reverseroll, without the need to redesign the roller shade or use custom parts.A standard roll roller shade is installed with the shade materialrolling off the back side of the roller, showing the back of the fabricon the roller, as shown in FIG. 7. In a reverse roll, the shade materialrolls off the front of the roller, hiding the roller. Typically, astandard roll roller shade comprises different parts than a reverse rollroller shade. The roller shade 300 of the embodiments, however, can beassembled and installed as either a standard roll or a reverse roll.Pretensioning the roller shade 300 in a counterclockwise directionallows the roller shade 300 to be quickly and easily assembled andinstalled for a reverse roll configuration.

Moreover, the counterbalancing assembly 400 of the present embodimentcan be either installed on the left side of the roller tube 301 and thewindow, as shown in FIG. 7, or on the right side of the roller tube 301and the window. Typically, a left counterbalancing assembly will need tocomprise different parts than a right counterbalancing assembly,dictating how the roller shade needs to be installed in a window.Pretensioning the roller shade 300 in a clockwise direction, allows theroller shade 300 to be installed on the left side of the roller tube301. Pretensioning the roller shade 300 in a counterclockwise direction,allows the roller shade 300 to be installed on the right side of theroller tube 300. This is beneficial where the location of theinstallation dictates the orientation of the roller shade. For example,where motor installation and/or an electrical connection may only beaccomplished on the left side of the window.

In another embodiment, mounting brackets 430 a and 430 b may compriseratcheting mechanisms to allow technicians to adjust the roller shade300 during installation or maintenance. For example, the shade material303 may have slipped off the roller tube 301 during installation oroperation of the roller shade 300 such that excess material 303 willremain hanging after the roller shade 300 had finished the rolling upcycle. The limit nut 607 and stops 605 or 606 will prevent rotation ofthe roller shade with respect to the gudgeon pin 403, preventing manualadjustment of the roller tube 301. To solve this, the ratchetingmechanisms provided in the mounting brackets 430 a and 430 b allow thegudgeon pin 403 to rotate with respect to the mounting brackets 430 aand 430 b to roll up the excess shade material 303 onto the roller tube301 until its correct position is reached. This ratcheting mechanism,however, does not affect the operation of the roller shade 300 duringits rolling down or rolling up cycle. In another embodiment, a slipclutch mechanism may be used.

INDUSTRIAL APPLICABILITY

To solve the aforementioned problems, the aspects of the embodiments aredirected toward systems, methods, and modes for counterbalancing andpretensioning a roller shade to lower the torque load on the motor ofthe roller shade throughout the rolling up or rolling down cycles.

The disclosed embodiments provide a system, and a method forcounterbalancing a roller shade with a counterbalancing assembly havinga pretensioned torsion spring and sizing and pretensioning the spring tolower the torque load on the motor of the roller shade throughout therolling up or rolling down cycles. It should be understood that thisdescription is not intended to limit the embodiments. On the contrary,the embodiments are intended to cover alternatives, modifications, andequivalents, which are included in the spirit and scope of theembodiments as defined by the appended claims. Further, in the detaileddescription of the embodiments, numerous specific details are set forthto provide a comprehensive understanding of the claimed embodiments.However, one skilled in the art would understand that variousembodiments may be practiced without such specific details.

Although the features and elements of aspects of the embodiments aredescribed being in particular combinations, each feature or element canbe used alone, without the other features and elements of theembodiments, or in various combinations with or without other featuresand elements disclosed herein.

This written description uses examples of the subject matter disclosedto enable any person skilled in the art to practice the same, includingmaking and using any devices or systems and performing any incorporatedmethods. The patentable scope of the subject matter is defined by theclaims, and may include other examples that occur to those skilled inthe art. Such other examples are intended to be within the scope of theclaims.

The above-described embodiments are intended to be illustrative in allrespects, rather than restrictive, of the embodiments. Thus theembodiments are capable of many variations in detailed implementationthat can be derived from the description contained herein by a personskilled in the art. No element, act, or instruction used in thedescription of the present application should be construed as criticalor essential to the embodiments unless explicitly described as such.Also, as used herein, the article “a” is intended to include one or moreitems.

All United States patents and applications, foreign patents, andpublications discussed above are hereby incorporated herein by referencein their entireties.

ALTERNATE EMBODIMENTS

Alternate embodiments may be devised without departing from the spiritor the scope of the different aspects of the embodiments. Theembodiments described herein may be used to counterbalance andpretension motorized roller shades as well as manual roller shades orsemi-manual roller shades, which roll up or roll down by pulling ortugging on a hem bar or by pulling on a chain. The embodiments describedherein may be used for covering windows as well as doors, wall openings,or the like. The embodiments described herein may further be adapted inother types of window or door coverings, such as inverted rollers, Romanshades, Austrian shades, pleated shades, blinds, shutters, skylightshades, garage doors, or the like.

Moreover, the process described herein for determining the number ofpreset pretensions and for pretensioning the spring is not meant tolimit the aspects of the embodiments, or to suggest that the aspects ofthe embodiments should be implemented following this process. Thepurpose of the aforementioned process is to facilitate the understandingof one or more aspects of the embodiments and to provide the reader withone or many possible implementations of the processes discussed herein.The steps performed during the pretensioning process are not intended tocompletely describe the process but only to illustrate some of theaspects discussed above. It should be understood by one of ordinaryskill in the art that the steps may be performed in a different orderand that some steps may be eliminated or substituted.

1. A roller shade comprising: a roller tube; a gudgeon pin comprising afirst stop and a second stop; a gudgeon body rotatably connected aboutthe gudgeon pin and operably connected to the roller tube, wherein thegudgeon body comprises a through bore; a limit nut operably connected tothe gudgeon body and adapted to axially travel along the gudgeon pin,within the through bore and between the first stop and the second stop;a pretensioned spring comprising a first end and a second end and thespring longitudinally extending therebetween, wherein the limit nutabuts the first stop or the second stop thereby locking pretension inthe pretensioned spring; a first spring carrier connected to the firstend of the spring and operably connected to the gudgeon pin; and asecond spring carrier connected to the second end of the spring andoperably connected to the roller tube; wherein during pretensioning ofthe pretensioned spring, the roller shade comprises: the second springcarrier positioned within the roller tube such that the second springcarrier is operably connected to the roller tube; the gudgeon bodypositioned outside the roller tube; the gudgeon body rotating withrespect to the roller tube, thereby causing the limit nut to rotate andaxially travel in a first direction, until the limit nut comes incontact with the first stop or the second stop; after the limit nutcomes in contact with the first stop or the second stop, the gudgeonbody further rotating with respect to the roller tube a predeterminednumber of pretension turns, thereby causing the first spring carrier andthe first end of the spring to rotate with respect to the second springcarrier and the second end of the spring; and the gudgeon body insertedinside the roller tube thereby locking the pretension.
 2. The rollershade of claim 1, wherein rotation of the roller tube to roll down theroller shade causes rotation of the second end of the spring in a firstdirection with respect to the first end of the spring, therebytensioning the spring.
 3. The roller shade of claim 2, wherein rotationof the roller tube to roll up the roller shade causes rotation of thesecond end of the spring in a second direction, opposite to the firstdirection, with respect to the first end of the spring, therebyreleasing the tension in the spring.
 4. (canceled)
 5. The roller shadeof claim 1, wherein the pretensioned spring comprises a predeterminednumber of pretension turns N_(p) determined according to the followingformula: $N_{p} = \frac{T_{min\_ offset}}{k}$ where, T_(min) _(_)_(offset) is substantially equal to, or offset by a predetermined amountfrom, a minimum amount of torque required to finish rolling up theroller shade, and k is substantially equal to a torque slope of theroller shade.
 6. The roller shade of claim 5, wherein the torque slope kof the roller shade is determined according to the following formula:$k = \frac{T_{\max} - T_{\min}}{N_{t}}$ where T_(max) is substantiallyequal to a maximum amount of torque required to start rolling up theroller shade, T_(min) is substantially equal to the minimum amount oftorque required to finish rolling up the roller shade, and N_(t) is anumber of turns it takes to fully roll up the roller shade.
 7. Theroller shade of claim 6, wherein T_(max) and T_(min) are determinedaccording to the following formulas:T _(max) =r _(rt)×(w _(sm) +w _(hb)) T _(min) =r _(sm) ×w _(hb) wherer_(rt) is a radius of the roller tube, w_(sm) is a weight of a shadematerial, w_(hb) is a weight of a hem bar, and r_(sm) is a radius of theshade material when it is fully wrapped around the roller tube. 8.(canceled)
 9. The roller shade of claim 1, wherein the gudgeon pincomprises a proximal portion, a middle portion, and a distal portion,wherein the first stop is disposed between the proximal portion and themiddle portion, and wherein the second stop is disposed between themiddle portion and the distal portion.
 10. The roller shade of claim 1,wherein the gudgeon body is rotatably connected about the gudgeon pinvia at least one ball bearing.
 11. The roller shade of claim 10, whereinthe gudgeon body comprises at least one ball bearing cavity dimensionedto receive the at least one ball bearing therein.
 12. The roller shadeof claim 1 further comprising a spring mandrel connected to the gudgeonpin, wherein the spring is mounted about the spring mandrel.
 13. Theroller shade of claim 1, wherein the gudgeon body comprises a wheel withan external surface that contacts an inner surface of the roller tube.14. The roller shade of claim 1, wherein the gudgeon body comprises aflange radially extending therefrom that prevents the gudgeon body fromsliding entirely into the roller tube.
 15. The roller shade of claim 1,wherein the gudgeon body further comprises a plurality of teethextending circumferentially about an external surface of the gudgeonbody that form a friction fit between the external surface of thegudgeon body and an inner surface of the roller tube.
 16. The rollershade of claim 1, wherein the gudgeon body further comprises a pluralityof channels extending circumferentially about an external surface of thegudgeon body that mate with complementary projections radially extendingfrom an inner surface of the roller tube.
 17. The roller shade of claim1, wherein the gudgeon pin comprises a gudgeon pin tip disposed on aterminal end of the gudgeon pin that attaches to a mounting bracket. 18.The roller shade of claim 1, wherein at least one of the first stop andthe second stop comprises at least one of a ring, a pin, a screw, or anycombination thereof.
 19. The roller shade of claim 1, wherein thegudgeon pin and the limit nut are threaded and wherein the limit nut isthreadably connected to the gudgeon pin.
 20. The roller shade of claim1, wherein the through bore comprises a cross-section having a shapethat complements and mates with a shape of the limit nut.
 21. The rollershade of claim 20, wherein the limit nut and the cross-section of thethrough bore comprise the shape selected from the group consisting of ahexagon, a triangle, a square, a heptagon, an octagon, and a star. 22.The roller shade of claim 1, wherein the gudgeon pin travels axiallywithin the through bore and wherein the first stop and the second stoplimit the axial travel of the gudgeon pin with respect to the gudgeonbody.
 23. The roller shade of claim 1, wherein the second spring carriercomprises a wheel with an external surface that contacts an innersurface of the roller tube.
 24. The roller shade of claim 23, whereinthe wheel of the second spring carrier is dimensioned such that it isoperably connected to the roller tube and can axially travel within theroller tube.
 25. The roller shade of claim 23, wherein the wheel of thesecond spring carrier comprises a plurality of channels extendingcircumferentially about its external surface that mate withcomplementary projections radially extending from an inner surface ofthe roller tube.
 26. The roller shade of claim 1, wherein the springcomprises a torsion spring.
 27. The roller shade of claim 1, wherein theroller shade is rolled up or rolled down by pulling or tugging on a hembar, by pulling on a chain, or via a motor.
 28. A roller shadecomprising: a roller tube; a gudgeon pin comprising a first stop; agudgeon body rotatably connected about the gudgeon pin and operablyconnected to the roller tube, wherein the gudgeon body comprises athrough bore; a limit nut operably connected to the gudgeon body andadapted to axially travel along the gudgeon pin within the through bore;a pretensioned spring comprising a first end and a second end and thespring longitudinally extending therebetween, wherein the limit nutabuts the first stop thereby locking pretension in the pretensionedspring; a first spring carrier connected to the first end of the springand operably connected to the gudgeon pin; and a second spring carrierconnected to the second end of the spring and operably connected to theroller tube; wherein the limit nut abuts the first stop when the rollershade is in a rolled up position, and wherein rotation of the rollertube to roll down the roller shade causes the limit nut to axiallytravel along the gudgeon pin, within the through bore, and away from thefirst stop; wherein during pretensioning of the pretensioned spring, theroller shade comprises: the second spring carrier positioned within theroller tube such that the second spring carrier is operably connected tothe roller tube; the gudgeon body positioned outside the roller tube;the gudgeon body rotating with respect to the roller tube, therebycausing the limit nut to rotate and axially travel in a first direction,until the limit nut comes in contact with the first stop; after thelimit nut comes in contact with the first stop, the gudgeon body furtherrotating with respect to the roller tube a predetermined number ofpretension turns, thereby causing the first spring carrier and the firstend of the spring to rotate with respect to the second spring carrierand the second end of the spring; and the gudgeon body inserted insidethe roller tube thereby locking the pretension.
 29. (canceled)
 30. Aroller shade comprising: a roller tube; a gudgeon pin comprising a firststop; a gudgeon body rotatably connected about the gudgeon pin andoperably connected to the roller tube, wherein the gudgeon bodycomprises a through bore; a limit nut operably connected to the gudgeonbody and axially travels along the gudgeon pin within the through bore;a first spring carrier operably connected to the gudgeon pin; a secondspring carrier operably connected to the roller tube; and a pretensionedspring comprising (a) a first end connected to the first spring carrier,and (b) a second end connected to the second spring carrier; whereinduring pretensioning of the pretensioned spring, the roller shadecomprises: the second spring carrier positioned within the roller tubesuch that the second spring carrier is operably connected to the rollertube; the gudgeon body positioned outside the roller tube; the gudgeonbody rotating with respect to the roller tube, thereby causing the limitnut to rotate and axially travel in a first direction, until the limitnut comes in contact with the first stop; after the limit nut comes incontact with the first stop, the gudgeon body further rotating withrespect to the roller tube a predetermined number of pretension turns,thereby causing the first spring carrier and the first end of thepretensioned spring to rotate with respect to the second spring carrierand the second end of the pretensioned spring; and the gudgeon bodyinserted inside the roller tube thereby locking the pretension.
 31. Amethod for pretensioning a spring of a roller shade including a rollertube, a gudgeon pin having a first stop, a gudgeon body, a limit nut, afirst spring carrier, and a second spring carrier, the methodcomprising: positioning the gudgeon body and the first spring carrieroutside the roller tube, wherein the first spring carrier is operablyconnected to the gudgeon pin and to a first end of the spring;positioning the second spring carrier within the roller tube such thatthe second spring carrier is operably connected to the roller tube,wherein the second spring carrier is connected to a second end of thespring, rotating the gudgeon body with respect to the roller tube aboutthe gudgeon pin, thereby causing the limit nut to rotate and axiallytravel in a first direction along the gudgeon pin and within a throughbore of the gudgeon body, until the limit nut comes in contact with thefirst stop, after the limit nut comes in contact with the first stop,further rotating the gudgeon body with respect to the roller tube apredetermined number of pretension turns, thereby causing the firstspring carrier and the first end of the spring to rotate with respect tothe second spring carrier and the second end of the spring; andinserting the gudgeon body inside the roller tube thereby locking thepretension.
 32. The method of claim 31, wherein the predetermined numberof pretension turns N_(p) is determined according to the followingformula: $N_{p} = \frac{T_{min\_ offset}}{k}$ where, T_(min) _(_)_(offset) is substantially equal to, or offset by a predetermined amountfrom, a minimum amount of torque required to finish rolling up theroller shade, and k is substantially equal to a torque slope of theroller shade.
 33. The method of claim 32, wherein the torque slope k ofthe roller shade is determined according to the following formula:$k = \frac{T_{\max} - T_{\min}}{N_{t}}$ where T_(max) is substantiallyequal to a maximum amount of torque required to start rolling up theroller shade, T_(min) is substantially equal to the minimum amount oftorque required to finish rolling up the roller shade, and N_(t) is anumber of turns it takes to fully roll up the roller shade.
 34. Themethod of claim 33, wherein T_(max) and T_(min) are determined accordingto the following formulas:T _(max) =r _(rt)×(w _(sm) +w _(hb)) T _(min) =r _(sm) ×w _(hb) wherer_(rt) is a radius of the roller tube, w_(sm) is a weight of a shadematerial, w_(hb) is a weight of a hem bar, and r_(sm) is a radius of theshade material when it is fully wrapped around the roller tube.